FM Modulation Math Question?

Question

Here's my question:

A frequency modulator (FM) circuit with a modulation index of 5 generates an un-modulated carrier frequency of 10MHz with peak amplitude of 20V.

A sinusoidal signal of peak amplitude 10V and frequency 2kHz is connected to the modulating input of the FM circuit.

Determine the peak frequency deviation of the carrier.

Can someone show me the answers + the workings out so I can attempt it myself? I haven't a clue what formula to use.

Answer 1

Page 110 of Simon Haykins 4th edition of "Communication Systems" says (my paraphrase):

s(t) = A_c cos [2 pi f_c t + Beta sin (2 pi f_m t)]

where A_c is the amplitude of the carrier,

f_c is the unmodulated carrier frequency,

Beta is the modulation index,

f_m is the frequency of the modulating signal

Beta = delta_f over f_m,

and delta_f = k_f A_m,

where A_m is the amplitude of the modulating signal,

and k_f is the frequency sensitivity of the modulator, in units of Hertz per Volt.

Really, what you appear to be trying to solve, is the beta sine () product.  You're given Beta= 5, and f_m, and since a sine wave varies between +/- 1 regardless of f_m, the frequency will vary by +/- 5 radians.

Answer 2

http://www.rfcafe.com/references/electri...